Problem: Solve for $x$ and $y$ using elimination. $\begin{align*}-8x+4y &= 2 \\ -2x+3y &= -4\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-3$ and the bottom equation by $4$ $\begin{align*}24x-12y &= -6\\ -8x+12y &= -16\end{align*}$ Add the top and bottom equations. $16x = -22$ Divide both sides by $16$ and reduce as necessary. $x = -\dfrac{11}{8}$ Substitute $-\dfrac{11}{8}$ for $x$ in the top equation. $-8( -\dfrac{11}{8})+4y = 2$ $11+4y = 2$ $4y = -9$ $y = -\dfrac{9}{4}$ The solution is $\enspace x = -\dfrac{11}{8}, \enspace y = -\dfrac{9}{4}$.